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loris [4]
3 years ago
6

You want to help make snow cones at your school fair. Each paper cone has a radius of 4.5 centimeters. The height of one cone is

8.3 centimeters. What is the volume of one cone? Use 3.14
Mathematics
1 answer:
skad [1K]3 years ago
3 0
Hello there.

You want to help make snow cones at your school fair. Each paper cone has a radius of 4.5 centimeters. The height of one cone is 8.3 centimeters. What is the volume of one cone? Use 3.14
176.01

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while visiting a mountain, John approximated the angle of elevation to the top of a hill to be 25 degrees. Alfter walking 350 fe
strojnjashka [21]
There are several ways of going about this problem, but just know that it all boils down to triangles and the rules/laws of triangles.
So we start by making a large right triangle, because the hill is vertical with the horizontal ground, with 25° as the left angle (where John looks up to top), 90° is the right angle (where ground meets hill base). So we see that the top side of the triangle is the hypotenuse, and equals the line of sight from John to hilltop.
Now we've got additional information that if John walks 350ft towards the hill, his angle of elevation increases by 14. So that = 25+14 = 39. How does that possibly help us?? Well now we can make 2 triangles inside of the one we've already made. So that now we have the triangle base split between the left angle of 25° and where he stopped 350ft to the right of that.
Now the supplement of 39 is 141, and the remaining piece of that too left triangle = 180-25-141 = 14. What does that mean? Well now we have a triangle, where we know all 3 angles and 1 side --> we can find another side by the law of sines:
If a, b and c are the lengths of the legs of a triangle opposite to the angles A, B and C respectively; then the law of sines states:
a÷sinA = b÷sinB = c÷sinC
We really need the hypotenuse to then find our hill height, so we'll make hypotenuse = side b in attached image. That being so, then its opposite angle (B) = 141. And the top right angle (C) = 14 with its opposite side (c) = 350ft.
Now we only need b÷sinB = c÷sinC
So b/sin141 = 350/sin14 --> b = 350sin141/sin14 = 350×.63/
b = 220.3/.24 = 910.47 ft
Now that's our hypotenuse, so using our original large right triangle, we can use right triangular trig. to solve. Let's make the right side, our hill height, equal to x.
Sin ¥ = opp. side / hypotenuse -->
Sin ¥ = x / hypotenuse
Sin25 = x / 910.5
x = 910.5×sin25 = 910.5×.423
x = 384.8 ft

3 0
3 years ago
The drama club sold 209 evening show tickets for $18.50 each and some afternoon show tickets. They want to make $5,700 for the t
Zina [86]

Answer:

156

Step-by-step explanation:

209x18.50=3866.5

5700-3866.5=1833.5

1833.5÷11.75=156.04

3 0
2 years ago
What is the surface area of the square pyramid represented by the net?
Dimas [21]

Answer:

<h2>7,938 Is the Area, do you need the perimiter?</h2>

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
Work out the gradient of the line joining the points (2, 3) and (5,7)
Debora [2.8K]

Answer:

The gradient of the line joining the points P(x,y) = (2,3) and Q(x,y) = (5,7) is \frac{4}{3}.

Step-by-step explanation:

The gradient of the line joining two distinct point on a plane is represented by the slope of a secant line (m_{PQ}), that is:

m_{PQ} = \frac{y_{Q}-y_{P}}{x_{Q}-x_{P}} (1)

If we know that P(x,y) = (2,3) and Q(x,y) = (5,7), then the gradient of the line is:

m_{PQ} = \frac{7-3}{5-2}

m_{PQ} = \frac{4}{3}

The gradient of the line joining the points P(x,y) = (2,3) and Q(x,y) = (5,7) is \frac{4}{3}.

4 0
3 years ago
Let sin(2x) = cos(x), where 0° ≤ x &lt; 180°. What are the possible values for x?
lions [1.4K]

Answer:

The possible values of x are 90°, 30° and 150°.

Step-by-step explanation:

Given that,

sin(2x) = cos(x) where 0° ≤ x < 180°

We know that, sin(2x) = 2 sinx cosx

2 sinx cosx = cosx

Subtract cosx on both sides

2 sinx cosx - cosx = 0

cosx (2sinx-1)=0

It means, cosx = 0 and (2sin x -1 ) = 0

cos x = cos0           and        sinx = 1/2

x = 90°                     and        x = 30°, 150°

Hence, the possible values of x are 90°, 30° and 150°.

6 0
3 years ago
Read 2 more answers
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